The evolution of disease resistance and immune function may be limited if increased immunocompetence comes at the expense of other fitness-determining traits. Both the maintenance of an immune system and the deployment of an immune response can be costly, and the observed costs may be evaluated as either physiological or evolutionary in origin. Evolutionary costs of immunological maintenance are revealed as negative genetic correlations between immunocompetence and fitness in the absence of infection. Costs of deployment are most often studied as physiological costs associated with immune system induction, however, evolutionary costs of deployment may also be present if genotypes vary in the extent of the physiological cost experienced.D. melanogaster. Phenotypes evaluated included fecundity, weight measures at different time periods and resistance to Providencia rettgeri, a naturally occurring Gram-negative pathogen of D. melanogaster. In the food-limited environment we found a negative genetic correlation between fecundity in the absence of infection and resistance, indicative of an evolutionary cost of maintenance. No such correlation was observed in the food-unlimited environment, and the slopes of these correlations significantly differed, demonstrating a genotype-by-environment interaction for the cost of maintenance. Physiological costs of deployment were also observed, but costs were primarily due to wounding. Deployment costs were slightly exaggerated in the food-limited environment. Evolutionary costs of immunological deployment on fecundity were not observed, and there was only marginally significant genetic variation in the cost expressed by changes in dry weight.In this study we analyzed evolutionary and physiological costs of immunity in two environments representing food-limited and food-unlimited conditions. Patterns of genetic variation were estimated in females from 40 'hemiclone families' isolated from a population of Our results suggest that the costs of immunity may be an important factor limiting the evolution of resistance in food-limited environments. However, the significant genotype-by-environment interaction for maintenance costs, combined with the observation that deployment costs were partially mitigated in the food-unlimited environment, emphasizes the importance of considering environmental variation when estimating patterns of genetic variance and covariance, and the dubious nature of predicting evolutionary responses to selection from quantitative genetic estimates carried out in a single environment. Understanding factors affecting susceptibility to infectious disease is the goal of many branches of the biological sciences. For the evolutionary biologist, these factors include the forces of mutation, gene flow, recombination, drift and selection and how these processes have shaped, and are currently shaping, genetic variation contributing to susceptibility to parasites and pathogens. The continued maintenance of genetic variation for disease resistance present in most populations -6 poses One hypothetical solution to this problem is that the rapid generation times of pathogens may provide them an evolutionary advantage over the host. Furthermore, for longstanding pathogen-host interactions, cycles of pathogen adaptation and host counter-adaptation may promote the rapid evolution of genes involved in defense and the maintenance of host polymorphisms through frequency dependent selection -9.In addition to the assumed advantage of pathogens over their hosts, and potential pathogen-host coevolution, evolutionary and ecological immunologists have more recently begun to consider the consequences of the host life history on patterns of disease susceptibility -15. The Pathogen defense is a multifaceted trait, including behavioral, morphological and physiological components ,19. HoweDrosophila melanogaster is a model system for much of our understanding of both constitutively expressed and inducible immune mechanisms including antimicrobial peptide production, phagocytosis of potential pathogens by insect hemocytes, the melanization reaction and encapsulation [The immune system of insects, while lacking the combinatorial specificity and antigenic memory characteristic of vertebrate immune function, is an effective mechanism of immunological defense providing protection against a wide variety of potential pathogens of bacterial, fungal, viral and multicellular parasitic origins. sulation ,20,21.But what are the costs of immunity? First, we must distinguish between maintenance costs and deployment costs, and second, whether these costs are physiological or evolutionary . MaintenA second distinction must be made between physiological costs and evolutionary costs. Physiological costs are evaluated either by examining the phenotypic correlation between fitness traits or through experimental manipulation. For example, the experimental manipulation of male sexual activity results in a decline in their immune function, consistent with the hypothesis that the maintenance of an immune system carries some physiological cost . PhysiolD. melanogaster, for example, experimental evolution of resistance to the parasitoid wasps Leptopilina boulardi and Asobara tabida revealed a genetic trade-off with larval competitive ability in crowded larval conditions [Evolutionary costs imply an underlying genetic basis to the observed cost and are evolutionary in the sense that they may act as brakes retarding the response to selection for immune efficacy. Evolutionary costs of immunological maintenance are revealed as negative genetic correlations between immunocompetence and the expression of other fitness components in the absence of infection ,14. In Dnditions ,4.D. melanogaster immunological defense against the parasitoid Asobara tabida caused declines in desiccation and starvation resistance and the magnitude of this cost varied among iso-female lines [Evolutionary costs of deployment indicate that genotypes vary in cost of immune system induction. Such costs would be revealed either as a significant genotype-by-immune challenge interaction when comparing fitness traits in immune challenged versus unchallenged individuals or by demonstrating that costs of deployment are exaggerated as a consequence of selection on immune system function. There are no previous attempts to evaluate evolutionary costs of immunological deployment. In le lines , howeverD. melanogaster was only revealed in a highly competitive environment [Environmental variation is known to affect the appearance and magnitude of both physiological and evolutionary costs of immunity. For example, reduced larval competitiveness in parasitoid-resistant ironment ,4, whileironment . In geneironment ,28. Furtironment ,30. In pironment .D. melanogaster and used them to estimate the evolutionary costs of immunological maintenance and deployment under both food-limited and food-unlimited environmental conditions. We evaluated maintenance costs as the genetic correlation between fecundity in the absence of infection and resistance to an experimental infection with the bacterium Providencia rettgeri. We estimated deployment costs as the change in fecundity following infection with live bacteria or heat-killed bacteria in comparison with both sterile wounding and uninjected controls. Our results indicate the presence of maintenance costs, but that these costs can be wholly mitigated in an environment in which food resources are not limiting. We also detected deployment costs, but as with maintenance costs, the decline in fecundity due to immune challenge was condition dependent.In this experiment we isolated 40 hemiclones from a natural population of P. rettgeri from 605 plates, and the dry weight of 5,248 females. Because of a labeling error, data for 2 of the hemiclone lines is missing from the fourth block of the experiment. Otherwise, sources of departure from the balanced design were random with respect to hemiclone line.The final data set included counts of 6,425 vials totaling 892,682 emerging offspring, colony counts of P. rettgeri, dry weight at emergence, dry weight at day 9, and the change in dry weight from emergence to day 9 are included in the analysis of maintenance costs. Hemiclone lines varied for all of these traits in both environments , resistance to ts Table  and 2.h2 = 0.06) was just less than half that seen in the yeast-unlimited environment (h2 = 0.15). Estimates of the coefficient of additive variation for fecundity in each environment were very similar, while the residual variation (CVR) in the yeast-limited environment was almost twice that observed in the yeast-unlimited environment  interaction . As with fecundity, there was evidence of a strong GxE interaction for female weight at day 9 post eclosion  were based on uninjected females. The heritabilities of dry weight at emergence and dry weight at day 9 (in either food environment) were all very similar, ranging from 0.21 to 0.27 . This correlation was absent in the yeast-unlimited environment . Using Fisher's z' transformation  we foundNo weight measure was significantly correlated with resistance Table . Dry weiWeight at emergence did not correlate with subsequent fecundity in either environment  and a marginally significant interaction between diet and injection . We therefore split the analysis between the two dietary manipulations  for the contrast repeated measures ANOVA compares the natural-log transformed fecundity in vial 3, prior to injections, with natural-log transformed fecundity in vials 4, 5, 6 and 7 separately. An initial analysis revealed significant interactions between diet and hemiclone line . This was mainly due to an approximate 10% decline in the fecundity of females in the first 28 hours after receiving an injection with either heat-killed bacteria or a sterile wound compared to the uninjected controls. In subsequent time periods the fecundity of females in the different injection treatments no longer differed , between bacteria injected females and females injected with a sterile needle (C2) and between females receiving an injection of any sort and uninjected females (C3). In the yeast-limited environment, only C3 showed a decline in the fecundity of injected females compared to uninjected females . However, in the first 28 hours after injection, when the cost was realized, the interaction was not significant .As previously discussed, evolutionary costs of immunological deployment are revealed as a genotype-by-challenge interaction, indicating genetic variation for the physiological cost experienced. In the yeast-limited environment, this interaction was marginally significant , although much less pronounced than that seen in the yeast-limited environment. However, unlike the situation in the yeast-limited environment, the effect was due primarily to the decline in fecundity in females receiving an injection with heat-killed bacteria, who showed a marginally significant decline compared to sterile-needle injected females  and a trend toward a significant decline compared to the uninjected females . There was no difference between sterile wounded females and uninjected females . Once again, the source of this effect was a difference apparent in the first day after injection, where females receiving an injection with heat-killed bacteria showed a strong decline in fecundity compared to both sterile wounded and uninjected females while sterile wounded and uninjected females were statistically indistinguishable . Examination of the a priori orthogonal contrasts showed no difference in the fecundity of females receiving injections with heat-killed bacteria versus injections with live bacteria . However, there was a decline in the fecundity of bacteria-injected females compared to sterile-needle injected controls . The effect seen in C2 makes the interpretation of the significance of the C3 comparison dubious. Post-hoc examination of the means for the different injection groups indicated that change in fecundity of females receiving an injection of bacteria (live or heat-killed) was lower than for uninjected females  and that there was no difference between uninjected and sterile needle injected females .Fecundity in the yeast-unlimited environment in the first 28 hours after injection was analyzed in the same manner as described for the yeast-limited environment .Once again, the line by injection interaction was marginally significant for the full model, but was not significant for the analysis of changes in fecundity in the first 28 hours after injection Table . To examIn terms of female dry weight at the end of the experiment, females receiving an injection (either with heat-killed bacteria or a sterile wound) had a lower weight than the uninjected controls in both environments Fig. , Table 7The experimental manipulation of yeast availability had a predictably large effect on female fecundity, with females in the yeast-unlimited environment . It is surprising that diet did not affect immune function given that a previous study, with a similar manipulation of food availability, found that females with ad libitum access to dietary yeast had dramatically improved immunity compared to females on a yeast-limited diet [Unlike fecundity and adult dry weight, there was no discernable effect of the environmental manipulation on immune function. Estimates of the number of bacteria recovered were nearly identical Table  and therted diet .D. melanogaster [E. coli, rather than the ability to slow the growth of a pathogenic bacterium. This also seems wanting as an explanation as the slower clearance of E. coli for females on the yeast-limited diet was mirrored by a more rapid death from an experimental infection with pathogenic Pseudomonas aeruginosa [This study differed in 3 ways that could potentially cause the disparity in outcomes. First, the studies used flies from different populations. However, given that there is little genetic differentiation among North American populations of nogaster  this doeruginosa .ad lib food conditions. However, it appears that the low food environment in the study of McKean and Nunney (2005) may have represented a greater limitation for females than in the present study. In support of this hypothesis, the fecundity of females in yeast-unlimited condition in McKean and Nunney (2005) was 6.7 times that of the yeast-limiting condition, compared to only a 2.5 fold increase seen in the present study. The results of McKean and Nunney (2005), utilizing the agar-cornmeal-molasses food, have recently been replicated  suggesting that the effect of food availability on patterns of immune function is a threshold trait, and that past a certain level of food availability further improvements in immune function do not occur.A third explanation, and the one that seems most likely, is that there are differences in the conditions actually represented by the environmental manipulation performed. The 'standard' yeast-limiting vials used in this study were made with agar-dextrose-yeast media while in the study of McKean and Nunney (2005) standard, yeast-limiting vials were made with agar-cornmeal-molasses. In both studies it seems likely that the yeast-supplemented vials represented Our analysis revealed heritable variation for each of the phenotypes assayed. These heritability estimates represent the upper bound of estimates of the narrow sense heritability . There aDue to the very large number of flies needed for this experiment , we did not attempt to precisely control the larval density or to keep track of the source of maternal chromosomes. It seems unlikely that variation in larval density would inflate our estimate of the additive variance. The numbers of females laying eggs in the collection vials was quite low and because the females in these vials were fully wild-type, variation among vials in the density of eggs laid is expected to be random with respect to hemiclone genotype. It also seems unlikely that our estimate of the additive variance is inflated by the confounding of non-additive genetic variance arising from a pervasive sampling of full sibs, in violation of our assumption that test females were almost exclusively composed of half-sibs. The test females used within each block of the experiment are the offspring of 75 randomly sampled females from our base population . Assuming an equal contribution of daughters from each female, the probability that two randomly sampled test females within a particular test vial of 5 females are not full sibs is 0.998. Therefore, it is not likely that estimates of the additive variance are inflated due to violation of the half-sib assumption.breeding value of a gamete, while a half-sib design provides estimates based on the breeding value of an individual [D. melanogaster, where there is no recombination in males, the breeding value of a gamete could differ from the breeding value of an individual male if there are strong epistatic interactions between allelic variants at loci on different chromosomes [D. melanogaster, it is unlikely that such non-additive effects would inflate the additive variance. Furthermore, the present design is very similar to other quantitative genetic designs in D. melanogaster utilizing balancer chromosomes [i.e., the North Carolina II breeding design; [A third source of deviation from more standard quantitative genetic designs is unique to the clone-generator system itself . The expdividual ,40. For omosomes . HoweverOur estimates for the heritability of fecundity, immunity and dry weight in the two environmental conditions Table  are consA, rather than the heritability. In general, the low heritability of life history traits, such as fecundity, appears to arise from a greater residual variation rather than an absolute reduction in the additive genetic variance. Such an effect seems to explain why we see such a low estimate for the heritability of fecundity in the yeast-limited environment (h2 = 0.06) compared to the yeast-unlimited environment (h2 = 0.15); a comparison of CVA shows they are similar in the two environments, however, the CVR in the yeast-limited environment is twice that seen in the yeast-unlimited environment  and hemocyte load (h2 = 0.74 ± 0.06) are more than three times as high as our estimates of resistance to P. rettgeri in the yeast-limited (h2 = 0.12) and yeast-unlimited environment (h2 = 0.14). Similar observations of very high levels of heritability have been reported for the caterpillar Spodoptera littoralis (phenoloxidase (PO) activity: h2 = 0.69 ± 0.07; encapsulation: h2 = 0.62 ± 0.14 [h2 = 0.36 ± 0.08; PO activity: h2 = 0.65 ± 0.11; antibacterial activity: h2 = 0.63 ± 0.11; haemocyte density: h2 = 0.36 ± 0.08; [h2 = 0.69 ± 0.48 [Our estimates for the heritability of the ability to slow the growth of ri Table  are much2 ± 0.14 ), in the ± 0.08; ), and ine h2 = 0. ± 0.06 aAnopholes gambiae was much greater than observed for resistance to E. coli [The exact origin of such profound differences in the magnitude of the heritability estimates is unclear. One possibility is that functional measures of the effectiveness of an immune response may be quite different than measures of single effectors or components of the immune response . For exa E. coli .Evolutionary costs of immunological maintenance are revealed as negative genetic correlations between fitness components in the absence of infection and immune system function ,51. Our D. melanogaster selected for increased resistance to the larval parasitoids Asobara tabida or Leptipolina boulardi [The effect of environmental variation on evolutionary costs of immunological maintenance has also been observed in lines of boulardi ,4. Theseboulardi -31,52.An immunological cost of deployment is recognized as a reduction in fitness as a consequence of immune system activation ,15,53. TThe experimental design used here allows us to examine both the physiological and evolutionary costs of immunological deployment. Our results suggest the presence of short-term physiological costs of deployment Fig. , 6, 7. TD. melanogaster involves the production of antimicrobial peptides and the activation of enzyme cascades involved in wound repair. These induced responses to wounding could contribute to the observed fecundity cost. The cost could also arise as a consequence of physical damage. However, it would seem that physical damage would have longer-lasting effects on fecundity instead of the transitory effect observed here.Females in the yeast-limited environment were less fecund in the first 28 hours after injection, but fecundity returned to uninjected levels by 48 hours after infection Fig. . The decMicrococcus luteus (a Gram-positive bacterium) and Escherichia coli (a Gram-negative bacterium). The fecundity of these females was compared to sterile media injected controls. Wild-type, immune intact, females experienced a significant and long lasting decline in fecundity [Our results differ dramatically from those reported by Zerofsky et al. . In theiecundity .M. luteus and E. coli were mixed, heat-killed, centrifuged and then the needle dipped into this highly concentrated pellet. We used solutions containing heat-killed bacteria diluted to an OD610 ≈ 0.6, or live bacteria at a slightly lower concentration (OD610 ≈ 0.2). The apparent active and rapid down-regulation of immune responses [M. luteus and Gram-negative E. coli) could produce longer-lasting costs. Consistent with this is the observation that the E38, relish mutants  did not experience a cost of deployment [M. luteus, was intact.We suggest two hypotheses to explain the disparity in 1) distinguishing changes in fecundity in sterile-wound and bacteria injected females and 2) the lack of a long-term fecundity cost in this experiment. First, there was a tremendous difference in the amount of bacteria introduced to females in the 2 experiments. In the study of Zerofsky et al. , overnigesponses ,56 may mployment  even thoWe also observed a deployment cost in the yeast-unlimited environment, and as with the yeast-limited environment, this cost was short term, with fecundity returning to the level of uninjected controls within 48 hours. The unlimited access to dietary yeast affected both the magnitude and the type of cost experienced. First, the 5% decline in fecundity of bacteria-injected (either live or heat-killed) females in the first 28 hours after infection was less than the 11% decline observed for similarly challenged females on the yeast-limited diet. Second, in the yeast-unlimited environment a cost of immune system activation could be distinguished from a simple cost of wounding Tables , Fig. 3.Bombus terrestris, the acceleration of mortality following challenges with LPS and synthetic beads was only seen when bees were starved subsequent to the challenge and not in bees kept on a normal diet [Spodoptera littoralis caterpillars immune function declined, but the cost of nucleopolyhedrovirus increased, as a consequence of manipulations of dietary protein levels [ad libitum access to food does not appear to allow for complete mitigation of deployment costs as this and another study [There are other examples of food availability affecting deployment costs and also the cost of parasitism itself. For example, in the bumble bee, mal diet . Likewisn levels . Howeverer study  have demMycobacterium marinum [A physiological cost of deployment was also reflected in the decline in dry weight of females injected with heat-killed bacteria or given a sterile wound. This decline in weight was seen in both the yeast-limited environment, where there was a 3.7% decline in dry weight, and in the yeast-unlimited environment where females exhibited a 2.3% decline in weight compared to uninjected controls Table . This ob marinum . In that marinum  argued t marinum . Our resLastly, we did not find overwhelming evidence of evolutionary costs of immunological deployment. For fecundity, there were marginally significant hemiclone line by injection interactions for the full model in the contrast MANOVA  in the summer of 2004. The population was maintained as isofemale lines until August 2005, when we created a large outbred population from equal numbers of mated females from each of the lines. We maintained this population for 6 generations prior to isolating the hemiclones used in the experiment. In general, adaptation to laboratory conditions occurs very rapidly [We established the population of  rapidly -64. ThusDuring the first 5 generations of outbreeding, we placed 15 females and 15 males in each of 250 vials (N = 7500). After 24 hours we removed the adults from the vials leaving only the eggs. Twelve days later, we collected the next generation of adults and mixed evenly among vials. In the generation prior to establishing the hemiclones, we randomly assigned 6 males and 6 females from each of the 250 vials to one of 100 vials . We maintained the population in a similar manner  during cytogenetic cloning and amplification.D. melanogaster genome). Cytogenetic cloning relies on the absence of recombination in males and the use of so-called 'clone generator' (CG) females. The process of hemiclone isolation, amplification, and the creation of hemiclone families for quantitative genetic analysis is described in Figure We isolated a total of 100 hemiclones from our sample population and from this sample randomly chose 40 for use in this study. The sampling of hemiclones (cytogenetic cloning) has been previously described ,65. The In this study we examined immunological costs in females only. Experimental females were founded by crossing hemiclone males randomly to females from the base population. For each of the 40 hemiclone lines used in the study, 5 replicate vials of 10 hemiclone males combined with 15 virgin females from the base population were established and transferred every 24 hours for 2 days. In this crossing design it is expected that 1/2 of fertilized eggs will be inviable, thus these conditions will result in relatively low larval densities. Furthermore, variation in larval density among collection vials due to variation in female fecundity should be random with respect to the hemiclones and thus should not act to confound subsequent phenotypic assays.VA [We mixed the newly emerged virgin females from all 10 vials before placing them randomly in experimental vials (see below). These fully wild-type females share the same set of paternal chromosomes  and a random set of maternal chromosomes and mitochondria. Assuming that most of the sampled offspring are not full sibs, these 'hemiclone-families' are composed of half-sisters that, because they share the same paternal set of chromosomes, have a coefficient of relatedness of 0.5. For any phenotype of interest, the deviation of the hemiclone family mean from the population mean phenotype gives a direct estimate of the breeding value of a gamete. The correlation of breeding values for different traits, or for the same trait expressed in different environments, is the broad-sense genetic correlation and the heritability can be estimated from the among family variance, which provides an upper bound to the additive genetic variance, VA .Providencia rettgeri and fecundity in the absence of infection. Deployment costs were evaluated as the decline in female fecundity following injections with either live or heat killed P. rettgeri compared with both sterile needle injected and uninjected controls. The design described below, and shown in Figure Our goals were to measure the evolutionary costs of immunological maintenance and deployment in food-limited and food-unlimited environments. An outline of the experimental design is shown in Figure μl of water onto the surface of the food in standard vials. The vials were then allowed to dry for 2 – 3 days prior to use in the experiment. This amount of yeast was not exhausted during the 24 hours the females were in vials, thus this manipulation represents an ad libitum amount of food.We manipulated adult food availability by adding dietary yeast to 'standard' vials. Standard vials were made with equal amounts, by weight, of glucose and yeast and these represent yeast-limited, but not starvation conditions. Yeast-supplemented vials were made by placing 40 mg of yeast suspended in 50 μg using a Sartorius CP2P microbalance .We collected experimental, virgin females as described above and placed 5 per vial in 8 standard and 5 yeast-supplemented vials . We froze females from the 3 extra standard vials on the day of injections to examine patterns of variation in immune system gene expression, the results of which will be published elsewhere. We collected an additional 6 experimental females and froze them for subsequent analysis of female dry weight at emergence. On day 2, we transferred the females to a new vial containing 5 males randomly sampled from the base population. On day 4, we transferred the flies to a new vial  and discarded vial 2. On the afternoon of day 5, we injected the flies (see below) and placed them in vial 4. We then transferred the flies every 24 hours for 3 more days . On day 9, we transferred the flies out of vial 7 and into microcentrifuge tubes and flash-froze them for subsequent analysis of female dry weight at the end of the experiment. We counted the number of emerging offspring for each of vials 3 – 7 representing our estimate of female fecundity. We determined the dry weight of females at emergence and on day 9 by drying the flies in a drying oven for 24 hours, and then weighing each individual to the nearest 0.001 Providencia rettgeri, or heat-killed P. rettgeri. Controls for the analysis of deployment costs included both sterile-wounded and uninjected females. P. rettgeri is a Gram-negative bacterium in the family Enterobacteriaceae. Providencia species have been isolated from a number of different insects, including Drosophila [P. rettgeri strain used in this experiment from the hemolymph of a wild-caught D. melanogaster collected near State College, Pennsylvania, USA. This strain is pathogenic to Drosophila, meaning that it is able to grow rapidly and cause fly death when introduced into the hemocoel.On the day of infections, we injected the females with either live osophila . B. Lazz610 = 0.6 (for injections with heat-killed bacteria) or A610 = 0.2 (for injections with live bacteria). We heat-killed the bacteria by placing a culture at 65 C for 45 minutes prior to injections. To test the effectiveness of the heat killing process, we plated a 50 μl sample of each of these cultures and in no case were live bacteria observed. We injected the flies by piercing their thorax with a 0.1 mm minutien pin  dipped into either 1) a liquid culture of live P. rettgeri, 2) a liquid culture of heat-killed P. rettgeri or 3) sterile LB. We used separate needles for each injection treatment. Uninjected and injected females were handled in a similar manner with respect to the timing of CO2 anesthetization.On the evening prior to infections, bacterial cultures were initiated in sterile LB and allowed to grow overnight at 30 C. We diluted the resulting cultures to an optical density of Aμl of sterile LB and plating 50 μl of this homogenate on LB plates with an Autoplate 4000 spiral plater . The plates grew overnight at room temperature and we then counted the number of colony forming units (CFU) using the Q-Count detection system . We plated a total of 8 plates for each hemiclone line in each environment.For females receiving an infection of live bacteria, we estimated the bacterial load 28 hours after infection by homogenizing 3 females in 500 P. rettgeri, and fecundity in the absence of infection is indicative of an evolutionary cost of immunological maintenance. We estimated genetic correlations as the parametric (Pearson product-moment) correlations of least-square hemiclone line means for our phenotypes from mixed-model ANOVAs outlined below. The analysis of fecundity in the absence of an immune response is based on counts of emerging offspring from vial 3. This represents counts of emerging offspring from 8 vials in the yeast-limited diet and 5 vials in the yeast-unlimited diet within each of the 4 replicate blocks (n = 32 for the yeast-limited diet and n = 20 for the yeast-unlimited diet). Counts of emerging offspring were natural-log transformed in order to improve the fit to normality. We performed a mixed-model analysis of variance (ANOVA) on the natural log transformed counts of emerging offspring using the following model:As discussed above, a negative genetic correlation between immunological performance, assayed as the ability to slow the growth of pathogenic μ is the grand mean, Li is the fixed effect of the ith hemiclone LINE , Dj is the fixed effect of the jth DIET (j = yeast-limited or yeast-unlimited), (LD)ij is the LINE × DIET (genotype-by-environment) interaction, bk is the random effect of the kth BLOCK  and εijkl is the residual variance. Estimation of the LINE least-square means and measures of variation  for fecundity in the absence of infection were estimated for each environment separately by entering the effect of LINE as a random factor into the model. Breeding values, used to establish genetic correlations among traits, were calculated as the deviation of the LINE least-square means from the population mean.where P. rettgeri infection using a mixed-model analysis of variance (ANOVA) on the natural log transformed counts of P. rettgeri colonies with the following model:We analyzed resistance to Li is the fixed effect of the ith hemiclone LINE , Dj is the fixed effect of the jth DIET (yeast-limited or yeast-unlimited), (LD)ij is the LINE × DIET (genotype-by-environment) interaction, ik is the random effect of the kth INJECTOR , bl is the random effect of the lth BLOCK  and εijklm is the residual variance. Colony counts were natural-log transformed in order to improve the fit to normality. Again, we calculated the hemiclone LINE least-square means and measures of variation separately for each environment. For the analysis of genetic correlations, we calculated the breeding value for resistance by subtracting the LINE least-square mean from the population mean. Thus positive values indicate hemiclone lines in which fewer bacteria were recovered .where We also collected data on female weight. Weight data included weight at emergence, weight at day 9, and from these two measures we could also calculate the change in weight. We evaluated among hemiclone line variation in emergence weight using the following mixed ANOVA model:μ is the grand mean, Li is the fixed effect of the ith hemiclone LINE , bj is the random effect of the jth BLOCK  and εijkl is the residual variance.Where At the end of the experiment we weighed uninjected females along with females that had received either heat-killed bacteria or a sterile wound. We analyzed day 9 dry weights using the following model:μ is the grand mean, Li is the fixed effect of the ith hemiclone LINE , Dj is the fixed effect of the jth DIET (j = yeast-limited or yeast-unlimited), Ck is the fixed effect of the kth immune CHALLENGE , bk is the random effect of the kth BLOCK , il is the random effect of the lth INFECTOR  and εijkl is the residual variance. We included all 2-way interactions and the 3-way interaction in the model. We used a reduced model to estimate the heritability of dry weight at day 9, including only females in the uninjected group, split between the two diets. We analyzed weight gain during the experiment by first subtracting the emergence weight from the weight at day 9 of uninjected individuals within each diet and then applying the following ANOVA model:where Li is the fixed effect of the ith hemiclone line , Dj is the fixed effect of the jth DIET (yeast-limited or yeast-unlimited), (LD)ij is the hemiclone LINE × DIET (genotype-by-environment) interaction, and εijk is the residual variance.where Physiological costs of immunological deployment are recognized as a decline in fitness trait values as a consequence of immune system activation. Evolutionary costs of deployment are present if genotypes vary in the physiological cost experienced. We evaluated both of these costs using multivariate, repeated measures analyses. We first compared the natural-log transformed counts of emerging offspring of females receiving an injection of heat-killed bacteria and sterile needle injected and uninjected controls. The multivariate analysis of variance (MANOVA) was carried out by implementing the contrast function in JMP. The contrast response design creates an M-matrix comparing post-injection fecundity  to pre-injection fecundity  for each of the four days post injection. Independent variables in the model included the main effects of hemiclone line, diet and injection in addition to all of their two- and three-way interactions. We also included the effects of block, injector and the number of females in the vial. This last effect was included due to the attrition of flies during the experiment due primarily to escape during transfer but also due to death. In addition to examining results from the full model, tests of each column of the M-matrix compared pre-injection fecundity with fecundity 28, 48, 72 and 96 hours post-injection.a priori orthogonal contrasts designed to test specific hypotheses concerning the effects on fecundity of the different injections. The first contrast (C1) compared pre-injection and post-injection fecundity between females receiving an injection with live bacteria versus females that received an injection with heat-killed bacteria. This contrast tests whether changes in fecundity following injection differ depending on whether the flies received living or dead bacteria. The second contrast (C2) compares the combined means of females receiving bacteria (either living or dead) with females that received a sterile wound. This contrast tests whether costs associated with a response to bacteria can be distinguished from costs associated with wounding. Results from this analysis are only meaningful if the comparison in C1 was not significant. The third contrast (C3) compares the combined means of females that received an injection of any type  to uninjected females. Provided that the previous contrasts were not significant, C3 tests the effect of wounding on changes in fecundity following injection.We also had fecundity estimates for the first 28-hours post injection for females receiving an injection of live bacteria. We examined the potential deployment costs associated with the response to live bacteria restricted to a single day post-injection using the same contrast design within the MANOVA platform described above. In this analysis, the response design matrix is a vector of pre-challenge fecundity  contrasted with fecundity in the first 28 hours after challenge . The independent variables in this analysis are the same as described above for the full analysis across all time periods post-injection. However, in this analysis we constructed a set of KAM and CPY coordinated and carried out the experiment. KAM analyzed the results and drafted the manuscript. All authors participated in outlining the experimental design and read and approved the final manuscript.


Despite the fact that genetic imprinting, i.e., differential expression of the same allele due to its different parental origins, plays a pivotal role in controlling complex traits or diseases, the origin, action and transmission mode of imprinted genes have still remained largely unexplored. We present a new strategy for studying these properties of genetic imprinting with a two-stage reciprocal F Many traits important to agriculture, biology, and human health are complex in terms of the genetic machineries that determine trait formation and development. Broadly speaking, these machineries are equipped with a web of actions and interactions of numerous DNA sequence polymorphisms, modified or altered by environmental factors. To elucidate a detailed picture of the genetic architecture of complex traits, various molecular, statistical, and computational tools have been developed and used in the mapping and identification of specific genes underlying the traits Arabidopsis thaliana to identify the genetic variation due to epiallelic variants in flowering time and plant height. Epiallelic variation can also be studied by tracing parent-dependent differences of the same allele. If the same allele functions differently, depending on which parent the allele is derived from, a phenomenon known as genetic imprinting or parent-of-origin effect, this allele may be epigenetic. Previous studies have suggested that genetic imprinting results from an epigenetic mark of differential methylation set during gametogenesis To describe variation among individuals in the number or distribution of methylated nucleotides at specific gene sequences, a new term, called epialleles, has been coined The past several years have witnessed an intense interest in mapping and identifying the regions of the genome that contain imprinted sequence variants with genome-wide linkage and association studies. Cheverud et al. In this article, we develop a novel strategy for identifying imprinted genes and understanding the transgenerational changes of their effects with a three-generation pedigree. This pedigree is initiated by reciprocally crossing two contrasting inbred lines, leading to two different FSuppose there are two inbred lines that are sharply contrasting in a complex trait. Each line can serve as a maternal and paternal parent, thus allowing a reciprocal cross. An FAssume that each FUsing the iQTL demonstrated in The same QTL genotype is different from different mating types due to the genetic imprinting of the FFThus, a final genotypic value of an FThe four epigenetically different Ffamilies  are obseTo determine whether there is an iQTL for the complex trait can be tested with log-likelihood ratio approaches. We first tested whether a significant QTL exists in the four FAfter a significant QTL is determined, then the imprinting effect of the QTL can be tested using the following null hypothesis,The newly developed model was used to analyze a data set from a large-scale QTL analysis project in which mice serve as a model system to study survival time to hyperoxic acute lung injury (HALI) Phenotype differences between the Fdetected , which idetected . All therom  to  . TherefoThe second test concerns the imprinting effects expressed in the F to zero . Except ceptions . One is In sum, all the detected iQTLs show a similar pattern of genetic effect on HALI in the Fositive) . PronounTo examine the statistical behavior of the new model, we performed Monte Carlo simulation studies by mimicking the example of the Ffamilies , initiatew model . At the ple size . To bettIn part 2, the simulation was used to test the power of the new model and its false positive rates. The conditions used for power calculation were the same as described above. According to traditional Mendelian genetic theory, the maternally and paternally derived alleles of a gene should have a similar amount of expression because they carry the same DNA sequence. However, a growing number of studies suggest that alleles may be expressed from only one of the two parental chromosomes The attempts to characterize imprinting effects are affected by our incapacity to discern the effect of DNA methylation variants from that of DNA sequence variants using a mapping study. This issue was, however, resolved by comparing two reciprocal crosses in which the maternally- or paternally-derived version of the same allele at a gene can be identified However, to study the precise genetic mechanisms through which chromatin dynamics alter quantitative variation, a simple test of imprinting effects of iQTLs is not adequate. Rather, a detailed understanding of whether and how imprinting effects are transmitted across generations is crucial for determining the contribution of epigenetic modification to heritable phenotypic variation for a complex trait. In this article, we present a new strategy for estimating and testing imprinting effects of iQTLs and their transgenerational transmission through two-generation reciprocal crosses leading to four epigenetically different Ffamilies . The newWe formulated a mixture model-based likelihood for the imprinting effects of iQTLs flanked by markers in four epigenetically different Fdetected  when theThe model developed in this article will provide a useful tool for studying transgenerational imprinting inheritance and its impact on the variation in complex traits and diseases. As a first attempt of its kind, the model will need to be modified so as to broaden the scope of its application. Given its ubiquitousness in trait control, epistasis between different genes should be incorporated into the current model, helping to draw a comprehensive atlas of the genetic architecture for complex traits. Also, the expression of any genetic effects cannot be isolated from the environment in which organisms are reared Figure S12 families, initiated with two inbred lines AA and aa. The two inbred lines that serve as female (red) and male parents (blue) are crossed reciprocally to generate two F1 families. From each of these two families, two progeny, one being a female (red) and the other being a male (blue), are selected to make all possible crosses, leading to four different F2 families .A mating design generating four reciprocal F(0.04 MB EPS)Click here for additional data file.Figure S2The plot of log-likelihood ratio across the mouse genome composed of 19 autosomes and one sex chromosome. Ticks on the x-axis are molecular markers. The peaks of the profile, at which significant QTLs on chromosomes 1, 4, 9, and 15 are detected by the new model, are indicated by arrowed vertical lines. The critical threshold for claiming the existence of significant QTLs is indicated by a horizontal line.(0.03 MB EPS)Click here for additional data file.Methods S1Supporting Methods.(0.04 MB PDF)Click here for additional data file.


Finally, for the first time from real data, we provide estimates of functional genetic effects as sets of effects of natural allele substitutions in a particular genotype, which enriches the debate on the interpretation of genetic effects as implemented both in functional and in statistical models. We also discuss further implementations leading to a completely general genotype-phenotype map.Although the genotype-phenotype map plays a central role both in Quantitative and Evolutionary Genetics, the formalization of a completely general and satisfactory model of genetic effects, particularly accounting for epistasis, remains a theoretical challenge. Here, we use a two-locus genetic system in simulated populations with epistasis to show the convenience of using a recently developed model, NOIA, to perform estimates of genetic effects and the decomposition of the genetic variance that are orthogonal even under deviations from the Hardy-Weinberg proportions. We develop the theory for how to use this model in interval mapping of quantitative trait loci using Halley-Knott regressions, and we analyze a real data set to illustrate the advantage of using this approach in practice. In this example, we show that departures from the Hardy-Weinberg proportions that are expected by sampling alone substantially alter the orthogonal estimates of genetic effects when other statistical models, like F The rediscovery of Mendel's laws of inheritance of genetic factors gave rise to the research field of Genetics at the very beginning of the last century. The idea of traits being determined by the effects of inherited genes is thus the conceptual core of Genetics. After more than one century, however, we still lack a completely general mathematical description of how genes can control traits. Such descriptions are called genotype-phenotype maps, or models of genetic effects, and they become particularly cumbersome in the presence of interaction among genes, also referred to as epistasis. The models of genetic effects are necessary for unraveling the genetic architecture of traits—finding the genes underlying them and obtaining estimates of their individual effects and interactions—and for meaningfully using that information to investigate their evolution and to improve response to selection in traits of economical importance. Here, we illustrate the convenience of using a recently developed model of genetic effects with arbitrary epistasis, NOIA, to inspect the genetic architecture of traits. We implement NOIA for practical use with a regression method and exemplify that theory with a real dataset. Further, we discuss the state of the art of genetic modeling and the future perspectives of this subject. There is an increasing interest in Quantitative Genetics and Evolutionary Biology to identify genetic effects, and more particularly gene interactions, on a genome-wide scale and to understand its role in the genetic architecture of complex traits ∞ model Regarding now the first issue mentioned above—the models of genetic effects—the definition of the genetic effects in Haley and Knott's 2 population or into an outbred population of interest. Second, using the functional formulation of NOIA, it is possible also to express the genetic effects as effects of allele substitutions from reference individual genotypes—instead of from population means like in the statistical formulation. In other words, starting from the orthogonal genetic effects of a population or sample under study, which are the ideal ones for performing model selection and have a particular meaning, NOIA enables us to obtain the values of the genetic effects that are associated to other desired meanings and are useful, therefore, to inspect different aspects of the evolution of a population, or selective breeding for increasing or decreasing a trait values.The statistical formulation of the recently developed NOIA  model of genetic effects is orthogonal in situations where previous models are not—for departures from the Hardy-Weinberg proportions (HWP) at any number of loci—and it is therefore more appropriate choice for estimating genetic effects from data in genetic mapping 2 populations, to compute genetic effects in a non-ideal situation, under departures from the HWP. We address this issue by generating simulated populations that depart from the HWP in several degrees and analyzing them with NOIA and other models. We quantify the deviances from orthogonal estimates due to using models that assume ideal conditions in the populations under study, thus showing the practical convenience of using the NOIA model for performing real estimates of genetic effects in QTL experiments. Second, we develop an implementation of NOIA with HKR, allowing it for immediate practical use and illustrate its performance using an example with real data. By this example we provide estimates of genetic effects with different meanings and, for the first time, functional estimates of genetic effects—using an individual genotype as reference—from a real data set. We discuss on how this feature opens new possibilities of using real data to analyze important topics in Evolutionary Genetics.Our motivation for this communication is to show how to use models of genetic effects to obtain estimates of genetic effects from data that have the desired meaning of any particular scientific purpose. To this end we first inspect how much of a difference it makes to use the classical models for ideal populations, such as ideal F2), the genetic effects of a two-locus and two-allele genetic system , αB and δB. The estimates in this group decreased with increasing departures from HWP. The third group contains the remaining three genetic effects, δA, δα and δδ, whose estimates are not affected by departures from HWP at locus B. The genetic effects measured by the G2A model show the same qualitative behavior described above for NOIA , but are quantitatively different. The reason for this is that G2A can adapt the measurements to the changes in the allele frequencies of the population, but not to the precise departures of the genotype frequencies from the HWP. The genetic estimates obtained using the F2 model always give the same values independently of the genetic constitution of the population. The F2 thus fails to capture the effects of departures from HWP at all. Thus, unless when the studied population is an ideal F2 . For orthogonal models, the sum of the three components of variance gives the total genetic variance—which in this case equals the phenotypic variance, since there is no environmental variance in the simulated populations. Here, this is only observed for the variances computed using NOIA. The other two models are not orthogonal in the populations under study , and thus there exist covariances between the genetic effects that would need to be accounted for to obtain the true genetic variance of the population 2 models is, thus, non-orthogonal. The G2A leads to a greater departure form an orthogonal decomposition of variance than the F2 model by the particular kind of departures from HWP simulated here. Both the G2A and F2 models underestimate the additive variance and therefore also the heritability of the trait in the simulated populations.A and B) genetic system with epistasis affecting growth rate in an F2 cross between Red junglefowl and White leghorn layer chickens A departs significantly from the HWP when considered alone, but not when correcting for multiple testing . 2 and G2A differ substantially from these of NOIA . This example with real data, thus, shows that it makes a substantial improvement to use NOIA to compute genetic effects and variance decomposition in QTL mapping experiments over the classical models of genetic effects designed to fit ideal experimental situations.For illustrating the advantage of using NOIA for analyzing experimental data, we reanalyze a two-locus , relative to the expected value without epistasis, which is a decrease in roughly 20 grams from the Red junglefowl. In total, this makes the phenotype of the White leghorn layer 20 grams higher than the Red junglefowl. However, for inspecting if this results support the White leghorn layer alleles being likely to reach fixation we also need to consider the phenotypes of the heterozygotes. Interactions involving dominance in locus B are all negative, thus favoring the fixation of the White leghorn layer allele, B2. The role of allele A2 is not as obvious, since da is positive. The genotypic value of “A1A2B2B2” is roughly 30 grams higher than the Red junglefowl (computed again from G = S⋅E) and ten grams higher than the pure White leghorn layer. The expected, therefore, would be that the two alleles segregate at locus A. The standard deviations of the estimates are however rather large and thus do not rule out the possibility of fixation of the White leghorn layer allele at locus A.For analyzing what would happen if eventually the two mutations were present at the same time in the population, we have to consider also the interaction effects. The double homozygote for White leghorn layer allele increases the phenotype with roughly forty grams  the ones with the reference of the mean of an ideal F2 population. Further, as illustrated in the example with real data, it is possible to transform statistical estimates of genetic effects into functional ones, using a particular reference genotype. Another situation in which these transformations are valuable is, for instance, in a three-locus genetic system with pairwise epistasis. In this case, NOIA would easily permit to consider only the significant genetic effects and to re-compute the genotypic values only from the significant genetic effects (assuming the non-significant third-order interactions to be zero).One example of the previous is removing the characteristics of the data that are not supposed to be properties of a target population from the estimates. The departures from HWP of the experimental data we dealt with in this article are in fact supposed to be only due to sampling, instead of being caused by real Hardy-Weinberg disequilibrium in the Fe.g.e.g.2 experimental population, into functional genetic effects as allele substitutions performed from a reference individual. Concerning these functional estimates of genetic effects, we have shown in the previous section how they can improve the understanding of the genetic system by inspecting a two-locus model obtained from real data. Notice that when changing the reference of the model, the genetic effects can change their magnitudes and even their signs . When performing IM for searching for the positions and estimates of genetic effects in QTL mapping experiments, missing data occurs at two levels. First, the genotype of the QTL located in a marker interval is not known and needs to be estimated from the observed flanking marker genotypes. Second, in most experimental datasets there are missing genotypes for many genetic markers that can be imputed from genotypes at closely linked informative markers. Thus, the implementation of HKR with NOIA enables us to perform IM with a regression method and using a model of genetic effects that is orthogonal regardless of how far the available data is from the HWP.et al.The HKR has been assessed as a good approximation of IM when dense marker maps are available and missing data are few and random et al.Models of genetic effects need to be further generalized. Two important cases that need to be accounted for are multiple-alleles and LD, which have been addressed in several recent publications dealing with statistical models of genetic effects. Yang A and B, generating several populations with the second locus affected by departures from the HWP in several degrees. The genotype-phenotype map corresponds to the phenotype mean of the population and all the genetic effects being equal to one in an ideal F2 population .We analyzed the simulated data by computing the genetic effects of the system using three models: NOIA, G2A and FSS (S5), in the HKR method, as we do with the F2 model in p11, p12 and p22 in the NOIA statistical formulation (S5) are the exact genotype frequencies at the considered loci. In the HKR, the genotype frequencies are not known, but can be estimated as:N is the number of individuals in the population under study. We implement this model in the general expression of the HKR (S4), in G* be the column-vector of observed phenotypes, G*k, k = 1,…,N, ε the corresponding vector of errors, and Z, which is an N×3-matrix whose rows are the vectors ωk (S4). With this notation, the general expression of regression (S4) is:SS matrix and the E vector can be extended as in Álvarez-Castro and Carlborg Z matrix can be extended as the row-wise Kronecker product of the matrices of the single loci, also as in Álvarez-Castro and Carlborg A and B) case, the ZAB matrix is an N×9-matrix that is built as:We recall the required theory behind the HKR and NOIA in et al.2 intercross of roughly 800 individuals between one Red junglefowl male and three White leghorn females. A simultaneous two-dimensional genome scan was performed to identify pairs of interacting loci regardless of whether their marginal effects were significant or not. We have studied in more detail one of the detected pairs involving QTL on chromosome 2 (486 cM) and 3 (117 cM), hereafter loci A and B respectively. This pair was selected for a number of reasons. First, these loci interact epistatically, in spite of showing no significant marginal effects in the studied population. Second, since they are located in different chromosomes, there is no physical linkage between them. Third, the genotype frequencies at locus A depart significantly from the HWP (p<0.05) when considered independently, but the departure is not significant after applying multiple testing correction accounting for the rest of the detected QTL. Thus, locus A is an example of the departure of the HWP that is expected in QTL experiments just due to sampling. The level of departure from the HWP for the evaluated pair roughly equals the 30% deviation in Carlborg A and B, using several models of genetic effects. First we used the F∞ model, which was the one also used by Carlborg et al.2 model, which was designed for F2 populations. Third, the G2A model, which can account for departures of the gene frequencies from ½, and finally the statistical formulation of NOIA, which can adapt to the genotype frequencies of the sample used for the estimation of QTL effects. In these analysis we have made use of the theory developed in this article: the implementation of HKR with NOIA. These developments enable us to deal both with missing data and with the estimation of genetic effects of positions inside the marker intervals.We have computed the genetic effects of the epistatic pair involving loci S matrix—the genetic-effect design matrix—of the orthogonal system, G = S1⋅E1, and the inverse of the S matrix in the new system, G = S2⋅E2:E1 can be expressed as functions of the estimates in E2 as:E2, can be computed from the ones in E1 as:E2, V2, from the vector of variances of the estimates E1, V1, we just rewrite (3) in algebraic notation as:Álvarez-Castro and Carlborg Text S1Background information on the HKR and NOIA. Concepts and equations related to the original formulation of the HKR and to the NOIA statistical formulation that will help the reader to deeper understand some details of the methods used in the article.(0.09 MB DOC)Click here for additional data file.


The authors analyze developmental, genetic, and demographic mechanisms by which populations tolerate changing environments and discuss empirical methods for determining the critical rate of sustained environmental change that causes population extinction. Many species are experiencing sustained environmental change mainly due to human activities. The unusual rate and extent of anthropogenic alterations of the environment may exceed the capacity of developmental, genetic, and demographic mechanisms that populations have evolved to deal with environmental change. To begin to understand the limits to population persistence, we present a simple evolutionary model for the critical rate of environmental change beyond which a population must decline and go extinct. We use this model to highlight the major determinants of extinction risk in a changing environment, and identify research needs for improved predictions based on projected changes in environmental variables. Two key parameters relating the environment to population biology have not yet received sufficient attention. Phenotypic plasticity, the direct influence of environment on the development of individual phenotypes, is increasingly considered an important component of phenotypic change in the wild and should be incorporated in models of population persistence. Environmental sensitivity of selection, the change in the optimum phenotype with the environment, still crucially needs empirical assessment. We use environmental tolerance curves and other examples of ecological and evolutionary responses to climate change to illustrate how these mechanistic approaches can be developed for predictive purposes.Global climate change, over-exploitation, and habitat alteration are causing sustained and consistent pressures on wild populations Two main approaches exist for studying the impact of environmental change on species persistence—niche modelling and mechanistic population modelling. On the one hand, “climate envelope models” (or “niche models”) are correlative and focused on the environment. Their conceptual background traces to Hutchinson's multidimensional representation of the niche On the other hand, mechanistic population modelling focuses on the biological processes that underlie population persistence. By combining evolutionary genetics and demography, the conditions that allow a population to maintain a positive intrinsic growth rate in the face of environmental change can be predicted theoretically Here, we propose a model of evolution and population growth to address how demographic and evolutionary constraints limit the persistence of a geographically isolated population under sustained environmental change. This model generalizes an earlier one by Lynch and Lande critical rate of environmental change: maximum rate of sustained environmental change that allows long-term persistence of a population, denoted as cη.environmental sensitivity of selection: change in the optimum phenotype with the environment. For a linear relationship, it is measured by the slope B.generation time: the average age of parents of a cohort of newborn individuals, denoted as T. With discrete non-overlapping generations, T is the mean time between successive reproductive episodes in the population.genetic variance: the genetic component of phenotypic variance σ2, or more precisely, “additive genetic variance” h2σ2, the statistically additive component of phenotypic variance determining the resemblance between offspring and parents, and the genetic response to selection.heritability: the proportion of phenotypic variance in a trait due to additive genetic effects, denoted as h2.intrinsic rate of increase: population growth rate in the absence of intra- or inter-specific competition. For a perfectly adapted population with mean phenotype at the optimum, the intrinsic rate of increase is denoted as maxr.norm of reaction: the expected phenotype of a given genotype as a function of the environment.phenotypic plasticity: direct influence of the environment on individual phenotypes through developmental mechanisms. For a linear norm of reaction plasticity is measured by the slope b.quantitative trait: continuously distributed phenotypic character, with phenotypic variance in a population determined by multiple polymorphic genes and environmental effects.stabilizing selection: natural selection such that individual fitness decreases with increasing phenotypic deviation from an optimum. Its strength is measured by γ.tolerance curve: fitness or performance as a function of the environment.There are three mechanisms by which a population can persist when its local environment changes: dispersal to track its preferred environment in space, genetic evolution to the new local conditions, or phenotypic plasticity ε  changes at a constant rate η in time. Adaptation to this changing environment is mediated by a quantitative trait z that determines fitness. Selection on multiple correlated traits also can be incorporated z, such that a given change in the environment directly modifies the phenotype of each individual by a constant amount. The rate of environmental change is expressed per unit time  instead of per generation.We assume that a continuous environmental parameter Under sustained environmental change, assuming constant genetic and phenotypic variance and strength of stabilizing selection, the rate of phenotypic evolution eventually reaches a steady state where the mean phenotype lags a constant distance behind the changing optimum phenotype . If thisσ2 and heritability h2 of the trait, the strength of stabilizing selection γ, and the maximum intrinsic rate of population growth maxr determined the critical rate of environmental change in the absence of phenotypic plasticity.The original model T. The remaining two parameters are the environmental sensitivity of selection B, which measures how changes in the environment influence the optimum phenotype, and phenotypic plasticity b, which quantifies the direct impact of the environment on development of individual phenotypes. The critical rate of environmental change for long-term persistence increases with decreasing absolute difference between the environmental sensitivity of selection and phenotypic plasticity. Although plasticity causes weaker natural selection on the trait and smaller genetic response to selection, this is more than compensated by the plastic phenotypic change that brings the mean phenotype closer to the optimum  of a population with optimum mean phenotype. Even if these parameters are not affected by the environmental change, they do constrain the rate of adaptation. Populations with longer generations must evolve faster per generation to adapt to a given rate of environmental change, and populations with a low maxr will reach extinction before they can adapt to rapid environmental change maxr per unit time is roughly inversely proportional to the generation time (1) Evolutionary potential. This measures how fast genetic evolution occurs for a given deviation of the mean phenotype from the optimum. The strength of stabilizing selection γ measures how the mean fitness decreases with the squared deviation from the optimum and also determines the strength of directional selection for a given deviation from the optimum. Stronger stabilizing selection (larger γ), although causing increased mortality, allows faster environmental change to be tolerated by causing faster evolution σ2 and heritability h2, determines how much genetic evolution is caused by a given strength of selection. Higher genetic variance allows persistence under stronger environmental change, because it allows the population to track its phenotypic optimum more closely. Although we focus on a single trait for simplicity, this may actually be a linear combination of measurable traits. In this case, the genetic variances of the original traits and their genetic covariances affect the magnitude of the genetic response to selection in any phenotypic direction (2) Biological impact of the environment. This links the environment to the biology of individuals in the species. Phenotypic plasticity describes the direct impact of the environment on the development of individual phenotypes. It may involve morphological, physiological or behavioural responses, which can occur on different time scales. For continuous environmental variables, plasticity usually is modelled using reaction norms, where the phenotype of a given genotype is plotted as a function of the environment b quantifies the degree of plasticity. The environmental sensitivity of selection, B, measures how the optimum phenotype changes with the environment, which for simplicity we also assume is a linear relationship. With no cost of plasticity, populations with b closer to B are likely to persist under higher rates of environmental change.(3) This model can be combined with environmental projections to ask whether future rates of environmental change will threaten the persistence of particular populations or species. Application of the model requires multiple steps, which previously have been undertaken in isolation or in combination, although all have rarely been completed together.Ecological investigation in the field is needed to identify traits that potentially determine adaptation to a specific environment. For instance, for ectotherms such as insects and reptiles, thermal adaptation may occur not only through physiological traits governing energy metabolism, but also through behavioural and morphological traits involved in movement between shaded and sunny patches γ has been estimated in many plant and animal taxa by regressing the fitness of individuals on their phenotypes maxr are needed to understand how phenotypic traits influence population dynamics. Analysis of natural selection has been extended to age- or stage-structured populations, allowing identification of parts of the life cycle where phenotypes most strongly influence demography The strength (and direction) of natural selection h2σ2) along the direction of natural selection limits the rate of evolution has motivated many studies. For instance, in the North American prairie plant Chamaecrista fasciculate, small genetic variance for a linear combination of traits has been predicted to limit the response to selection caused by climate change Drosophila species The question of whether genetic variation  directly to the environment, which makes it difficult to produce evolutionary predictions and to test them experimentally Environmental tolerance curves relating fitness (or performance) to abiotic environmental variables such as temperature We propose that incorporating phenotypically plastic traits, which are under stabilizing selection through their influence on lifetime fitness Thermal tolerance curves generally are strongly skewed, with fitness decreasing steeply as temperature approaches the critical thermal maximum The model in Box 2 assumes a linear reaction norm, implying that a given amount of environmental change always produces the same plastic phenotypic change. Plasticity is generally studied in the context of environments that vary in space or fluctuate in time with a stationary distribution, but little is known about plastic responses outside the usual range of variation. Extreme environments may disrupt the plastic response, such that the reaction norm may take any shape in environments that were rarely encountered before Phenotypic plasticity may entail several types of fitness costs to the organism independent of the expressed phenotype In the literature on tolerance curves, the cost of plasticity is generally expressed as a trade-off between tolerance breadth and fitness in the optimum environment, corresponding to the intuitive idea that the “Jack-of-all-trades is a master of none.” This has been modelled In the model of Box 2 and γ may depend on the environment  can cause the genetic variance (h2σ2) to depend on the environment Our model includes a number of simplifying assumptions. We assume a constant shape of the fitness function across environments, allowing only the optimum phenotype to change with the environment. However, the strength of stabilizing selection around the optimum phenotype Plasticity itself may evolve if it varies genetically, and new environments can cause directional selection on plasticity Finally, we considered a population that cannot disperse nor receive migrants from other populations experiencing different environments. We focused on this situation because it is one that is most commonly overlooked in niche modelling studies. Our model thus applies best to species with habitats restricted by dispersal barriers or species which disperse slowly relative to the rate of environmental change Our aim was to describe an approach based on evolutionary and demographic mechanisms that can be used to make predictions on population persistence in a changing environment and to highlight the most important variables to measure. While this approach is obviously more costly and time-consuming than niche modelling, its results are also likely to be more useful for specific purposes because it explicitly incorporates the factors that limit population response to environmental change.Aedes aegiptii in Australia. Egg desiccation was treated as a threshold trait, but the possibility of phenotypic plasticity or evolution of the threshold was not considered. These encouraging efforts call for more empirical studies where genetic evolution and phenotypic plasticity are combined with demography to make predictions about population persistence in a changing environment. The simple approach we have outlined is a necessary step towards a more specific and comprehensive understanding of the influence of environmental change on population extinction.The feasibility of such a mechanistic approach has been demonstrated by a few recent studies. Deutsch et al. Text S1A model of plasticity, evolution, and extinction in a changing environment.(0.48 MB PDF)Click here for additional data file.


In vitro experimentation provides a convenient controlled environment for testing biological hypotheses of functional genomics in cancer induction and progression. However, it is necessary to validate resulting gene signatures from these in vitro experiments in human tumor samples (i.e. in vivo). We discuss the several methods for integrating data from these two sources paying particular attention to formulating statistical tests and corresponding null hypotheses. We propose a classification null hypothesis that can be simply modeled via permutation testing. A classification method is proposed based upon the Tissue Similarity Index of Sandberg and Ernberg  that uses the classification null hypothesis. This method is demonstrated using the in vitro signature of Core Serum Response developed by  Integration of in vitro studies, i.e. experimental studies, with human “in vivo” gene expression studies is an area that is being considered more frequently in the functional genomic analysis of cancer. Hypotheses about cancer development, progression, and risk factors are difficult to test directly in a patient population. However, in experimental studies on cell cultures and model organisms, conditions can be specifically controlled to allow biological hypotheses to be tested. Integrating the results from such experiments with in vivo cancer signatures holds the potential to both infer activity of specific oncogenic pathways in vivo and to identify relevant effectors of oncogenic pathways.To begin to understand the mechanisms by which oncogenes cause cancer, studies have used gene-expression profiling to identify downstream targets of oncogenic pathways in cell-culture systems. Conceptually, this involves manipulating a gene in an in vitro system, measuring the global profile using gene expression technology and then trying to relate the in vitro gene expression profile to an in vivo gene expression profile. Such an approach was taken by Additionally, studies have used gene-expression profiling of cancerous growths induced in model organisms to examine tumor development or progression. Though model organism studies have the added difficulty of mapping orthologous genes between organisms, a difficulty not shared with tissue and cell cultures of human origin, there have been promising applications. For example, It is expected that in vitro/in vivo experiments such as those described in the previous two paragraphs will become much more commonplace in the future. Thus, it is critical to address statistical issues and to develop methods for integrating in vivo and in vitro genomic data so that inferences regarding transcriptional regulatory pathways in cancer can be generated. In this article, we discuss the statistical issues of the integration of these two types of datasets. We review various existing approaches and discuss their statistical advantages and disadvantages. In addition, we outline an approach for quantifying the predictive ability of a gene expression profile determined from an in vitro experiment based on the tissue similarity approach of One class of methods that has been popular in the literature for in vitro/in vivo genomic data analysis is the following. First, one generates ordered lists of genes using the in vivo expression data. One then generates a differentially expressed gene list using the in vitro data and studies the overlap between the two lists. The seminal examples of this are in There are some desirable features of the GSEA method. First, it utilizes all the information available in the in vivo gene expression data; no thresholding is done in that dataset. Second, a Kolmogorov-Smirnov statistic is used for the analysis, which is a non-parametric method and thus provides some robustness. However, there are several disadvantages to GSEA as well. For instance, note that there is thresholding done in the in vitro gene expression dataset to select the differentially expressed gene set. A potential improvement to the GSEA method, to avoid this thresholding, would be the following. First, one determines the common genes in the in vivo and in vitro datasets. One then takes the scores of differential expression from the in vitro data, finds the corresponding correlation scores (correlation with Cyclin D1) in the in vivo data and examines a scatterplot of the two variables. If the association is linear, then one tests for association using the Pearson correlation coefficient between the two variables. If instead the association appears nonlinear, then one could use a smoothing-spline based test . Such anBefore going further, let us consider the null hypothesis under consideration in the GSEA method, or the variants proposed above. Specifically, in the 0 is true; however, the two permutation schemes developed in the GSEA method do not do this. Permutation of the sample labels fails because the null hypothesis pertains to the population of genes in the two studies and not the relation of samples within a study. Additionally, The alternative hypothesis is that there is an association. In specifying the null hypothesis we uncover a more subtle disadvantage of the GSEA method—the determination of the distribution of the KS test statistic under the null hypothesis. Two variants of permutation testing have been proposed by There is an alternative approach to the GSEA method for integrative analysis of in vitro and in vivo data, which is what we focus on in the rest of the paper. It is based on ideas of classification and clustering since the goal in many genomic studies utilizing high-throughput expression technologies is to develop a signature that can discriminate between relevant classes or groups of samples. In general, demonstration of the predictive or prognostic ability of a classification signature on independent data sets is a crucial step in the validation of that signature . Thus, d0 class as the classification null hypothesis.The alternative is that at least one set of genes derived from the in vitro data is predictive. Notice that this null hypothesis is different from the null hypothesis described for the GSEA method. For clarity, we will refer to H0 class is true, then any set of genes derived from the in vitro expression profile data will have no ability to separate samples in the in vivo expression dataset with regard to a clinical outcome. Thus, we can take random sets of genes from the in vitro data and apply the classification algorithm of interest. If the classification null hypothesis is true, then all sets of genes, including the derived signature, should provide equal prediction performance.An advantage of the classification null hypothesis is that permutation testing becomes possible here. In particular if HThe classification null hypothesis has motivated the following algorithm that we have used in our previous work . Here weDerive a gene signature from the in vitro gene expression data;Select those genes from the in vivo expression data that are included in the in vitro signature and cluster the samples from the in vivo expression data into two groups using hierarchical clustering with average linkage clustering and Euclidean distance;Calculate the log-rank statistic for survival between the two groups of patients;Let L denote the size of the gene list in 1. Randomly choose L genes from the in vitro data as the gene signature. Continue with steps 2 and 3 above.Repeat steps 2–4 1000 times. Calculate the proportion of datasets in which the log-rank statistic is greater than the one calculated initially from the signature in step 1.The proportion calculated in step 5 will be the permutation p-value under the classification null hypothesis. This permutation scheme will form the basis of assessing significance for our proposed analytical scheme described in the next section. We note that one could also modify the GSEA procedure in a similar way, as shown in Notice that a limitation of the classification null hypothesis is that the alternative hypothesis states that there exists at least one signature from the in vitro expression data that is predictive in the in vivo expression data. In fact the experimentally derived gene list need not be a unique classifier. It has been recently noted that there are likely many gene signatures that have similar predictive power . It may The paper of The algorithm of To integrate the in vivo data, first map the in vivo samples into the same reduced space of the in vitro samples by again calculating the correlation between each eigenarray and in vivo sample array. To maintain scale in this correlation, the tumor samples are also standardized so that each gene has a mean expression of zero and a unit standard deviation. The distance between the in vivo tumor sample and each of the two consensus signatures, i.e. centroids, is calculated using Pearson correlation. Samples are classified with the experimental condition with whose centroid they correlate best.There are several differences between their and our implementations of TSI. First, in contrast to Since the gene signature on which the classification is based is determined from the in vitro data, and does not use the in vivo data, the statistical significance of any tests on the in vivo data can be accepted without bias. This is an example of using the in vitro data for the training dataset and the in vivo data for the testing dataset. Indeed, if this in vivo validation is not at least marginally significant it is not of interest to proceed further to test the classification null hypothesis.Using the TSI method, we develop a classification scheme from the in vitro signature. The null hypothesis of interest is again the classification null hypothesis as presented above. We thus propose the use of a permutation test to determine the utility of the gene signature in its classification ability. In the following we slightly modify the permutation test procedure described in the previous section to account for gene-gene correlation within the in vitro gene signature. Specifically, as it is likely that genes within a pathway are correlated, it is reasonable to assume that the significantly differentially expressed genes that comprise the in vitro signature are correlated. Finally, the permutation test for the TSI analysis has two interesting attributes against which the classification signature is compared. Specifically, in permuting the data, the TSI scores are recalculated using the randomly selected gene list and with each randomly selected set of genes there is a possibility of unclassified samples. Thus the classification is compared to: (1) the measure of association with predictive factors in vivo, and (2) the percentage of unclassified samples in vivo.For the purpose of demonstration we use, as the in vitro derived signature, the wound healing signature of http://smd.stanford.edu/cgi-bin/publication/viewPublication.pl?pub_no=293) . The data were normalized using loess normalization by print block within array . Sporadic breast cancer expression data and recurrence free survival information . Each of these experiments was normalized by global scaling per array. No imputation was done for missing data in the tumor sample data sets.Localized prostate tumor probe-set level expression measures and recurrence free survival information  were obton van’t  were obtUnigene Cluster ID number was used to map genes between platforms. Annotation information was acquired from SOURCE . If, forThe classifier was built using the CSR in vitro signature and the TSI algorithm, described in the previous section and in 0 class, we wish to see if the in vitro derived CSR signature has prognostic ability in vivo. Thus the prognostic ability of the CSR signature as a classifier was tested using univariate Cox regression; see According to HAccepting the above significant separation of the Kaplan-Meier curves as validation of the CSR signature in vivo, we proceed to test the classification null hypothesis using 1000 random samples from the genes in common between the in vivo and in vitro samples, see As depicted in The breast cancer samples appear to have a more well defined subset of unclassified samples, see One problem encountered in this analysis was the integration of gene expression data across microarray platforms. We attempted to compensate for this numerically by global standardization that centered the array-wise median values at zero. Furthermore, in the TSI algorithm genes were standardized to zero mean and unit standard deviation before being mapped into the reduced space. An additional complication, beyond numerical scaling, is that the differing array configurations between the in vitro and in vivo experiments mean that only those genes with Unigene ID numbers common to both data sets can be considered. This initially excludes ESTs from the in vitro signature as well as other features that do not have Unigene ID numbers. The signature is further reduced by focusing on only the common genes between data sets as determined by Unigene ID. We expect that there is correlation between the genes within the CSR signature and thus the loss of some genes from this signature will be tolerable.The most dramatic decrease in CSR genes available for the analysis was for the Finally, we turn our attention to the permutation testing depicted in 0 class. In the prostate samples, Next, consider the empirical p-value for testing HHere we have discussed the nature of hypothesis testing when integrating gene expression signatures derived from hypothesis driven in vitro studies with gene expression profiles of in vivo tumor samples. Assigning significance to classification results and associations is necessary to evaluate the utility of the in vitro signature in cancer development and progression as found in vivo. However, for accurate assessment of significance it is necessary to consider the underlying null hypothesis that is being tested. Though the permutation test has been widely accepted as a panacea for significance testing we discussed how the permutation must be done with care so that the underlying null distribution is appropriately reconstructed. We provide a method of assessing the classification potential of an in vitro signature using the TSI classifier of Although we have discussed the value of a well defined null hypothesis, the interpretation of the alternative hypothesis comes into play when the null is rejected. In particular, the alternative hypothesis for the classification null hypothesis is that at least one predictive signature exists. The number of such signatures is not known and thus the signature being tested need not be unique. We know from We have remarked at several points about the use of thresholding in the algorithms. Arbitrary thresholds used to select genes that are interesting biologically or signatures that are significant statistically may not always be satisfying. We briefly discussed how the concept of GSEA could be adapted to a regression model that would not require a strict definition of the in vitro gene set of interest. Yet, the TSI-type algorithm that we proposed still used thresholding of the in vitro data to produce a signature. This is not necessary for the sake of the algorithm and classification should still be possible using the entire gene signature of the in vitro samples. Ultimately the classifier is built on the correlation of the in vivo samples to composite signatures for each experimental condition in the reduced space.We again used thresholding in the classification of the in vivo samples by requiring a significant correlation with one of the experimental centroids. The threshold for significance was left at the typical level of p < 0.05, although this could be adjusted to achieve desired specificity and sensitivity in the classifier by dividing the in vivo samples into training and test sets and examining various thresholds. Alternatively, the correlation score could be used as a continuous variable in the Cox regression models. In this way those samples that were not classified in the dichotomous classification would contribute to the model.